This is a classic Chinese Tangram. Each of the people illustrated, and many convex polygons, can be made with the 7 pieces and there are hundreds of other puzzles based on this tangram.
Can you find a way to fold a sheet of paper so that you can cut out the tangram pieces accurately […]
Differences of Squares Investigation
1. What do you see in this picture?
Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .
2. What do you notice about the difference between squares of consecutive numbers?
Compare the differences between squares of numbers that differ by 1 […]
Two by Two Puzzle
Can you find numbers to replace the ? marks to solve this two by two multiplication puzzle? Can you explain how it works?
How does the diagram below connect with the multiplication?
Use the two grids to do the two multiplications:
72 × 25 […]
The histogram shows the number of children in each age group on a school bus. There are no children under 5 years and no children over 17 years. There are 6 children aged between 5 and 10 years . Explain why the class boundaries are 5, 11, 16 and 18. Complete the following table. […]
Make enlargements of the coloured shapes by fitting together four identical smaller shapes.
How much longer are the edges (the linear scale factor of the enlargement)?
How much bigger is the area (the area scale factor of the enlargement)?
Now look at the illustration of the 3-dimensional solids. One is […]
ALGEBRAREA Product of brackets and area
1. You have 2 blue shapes, 3 green and 5 brown. Describe their properties.
2. Find the areas in square units of the 3 pieces blue, green and brown.
3. Build one big geometrical shape using all 10 pieces, placing them edge to edge. Draw […]
1. For security John plans buy the minimum amount of Diamond Razor Mesh fencing material to fence around his dam and discourage entry. He sent his 15 year old son Mzu to measure the dam.
Mzu tells his Dad that this rectangular shape he has drawn of the dam and fence can help him.
The right angled triangles numbered 1, 2, 3 and 4 in the diagrams all have sides of length a, b and c. They are identical (congruent) copies of each other.
Cut 4 congruent right angled triangles from some scrap paper. Arrange them as shown in diagram […]
Doesn’t Add Up
Look at this square divided into four pieces : two identical triangles and two identical trapezia.
The edge of length 3 from each triangle matches with the edge of length 3 from a trapezium so that the four pieces from the square now occupy a rectangular space.
The square had side length 8 […]
Kite in a Square
ABCD is a square with edge 1 unit. AM=MB and O is the centre of the square.
Find the area of the kite.
Can you find this area by more than one method?
Click here to download the KITE IN A SQUARE worksheet
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